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E. Philip Krider

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William J. Koshak and E. Philip Krider

Abstract

A constrained, least-squares method for analyzing multiple-station measurements of lightning field changes (ΔEs) is introduced. Previous methods have attempted to fit the spatial pattern of lightning ΔEs using nonlinear models, such as a point charge (Q) or a point dipole (P) model. With the linear method, the ΔEs are described not by models but by a general volume charge distribution that is deposited on a large (40 × 40 × 20 km3) Cartesian grid above the measuring network. A linear system of equations is used to relate the measured ΔEs to the charges that are deposited at each grid point. With this approach, the information content of the measurements can be quantified by an eigenanalysis of the covariance matrix of the liner system. Constraints can be used to reduce the infinity of possible solutions to the linear system and also to reduce systematic biases that can be introduced by the method of solution. It is shown that a Landweber iterative method, derived from the general method of steepest descent, can be used to solve the linear system and that the resulting volume charge distributions are generally consistent with computer-simulated charge sources, when these sources are over the measuring network. The Landweber iteration has also provided solutions for natural lightning events that are consistent with Q- and P-model results.

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Elizabeth A. Jacobson and E. Philip Krider

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The electrical behavior of thunderstorms triggered by local heating and sea-breeze convergence, a low pressure disturbance, and a weak frontal passage has been studied at the NASA Kennedy Space Center, Florida. A nonlinear least-squares minimization procedure has been developed to describe changes in the total electrostatic field produced by lightning in terms of point charge models for the cloud charge distributions. The results of this analysis indicate that discharges to ground usually neutralize cloud charges in the range from −10 to −40 C. The computed charge altitudes for Florida are somewhat higher than for other geographical locations, 6 to 9.5 km, but the corresponding ambient air temperatures, −10 to −34°C, are similar. A large fraction of the discharges to ground show total field changes which are small or even reversed in polarity within 3 km of the discharges. An analysis of these cases suggests that ground discharges often neutralize a small positive charge, 0.5 to 4 C at altitudes of 1 to 3 km, in addition to the larger negative charge higher in the cloud.

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Nathan G. Parker and E. Philip Krider

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A digital video camcorder, a four-channel analog-to-digital (A/D) converter, and a GPS time/position receiver have been interfaced to a portable personal computer (PC) to provide a mobile data-collection platform for making precise time-synchronized optical and electromagnetic measurements of lightning with correlated video imagery. Optical waveforms and the associated electric field signatures are digitized with 14-bit resolution at a sampling frequency of up to 2.5 MHz, and entire flashes can be captured and stored with less than 280 ms of dead time between events. Digital video (DV) data can be recorded either on Mini-DV tape within the camera or directly in the PC using an IEEE 1394 “Firewire” serial data link. The video format has a standard 30 interlaced frames per second (33.3 ms per frame) and 720 × 480 pixels per frame, and in postprocessing the frames are deinterlaced to double the time resolution (to 16.7 ms). The system was tested on natural lightning during the summer of 2001 near Tucson, Arizona. Video images are shown of cloud-to-ground (CG) flashes, attempted leaders, and vertical and horizontal air discharges, and several examples of correlated optical and electric field waveforms are given. An analysis of 249 CG flashes shows an average of 1.46 strike points per CG flash, and shows that flashes with a visible attempted leader are more likely (by a factor of 2) to produce multiple strike points and less likely (by 1/3) to have a long continuing luminosity, but the statistics are limited. A subset of these data shows that the flash and stroke detection efficiencies (DE) of the U.S. National Lightning Detection Network (NLDN) near Tucson are about 61% and 36%, respectively, with a 24-ms coincidence criterion, and 71% and 41%, respectively, with a 33-ms criterion. The latter DE values are similar to DEs measured near Albany, New York, and agree with model predictions.

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Nicole M. Kempf and E. Philip Krider

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Relationships between cloud-to-ground (CG) lightning, as reported by the U.S. National Lightning Detection Network (NLDN), and surface rainfall, as reported by National Weather Service (NWS) cooperative observers, have been examined during the “great flood” of 1993. The daily precipitation volume per reported CG flash (CGF) over the greater Upper Mississippi River basin (GUMRB) ranged from 4.0 × 104 to 4.3 × 106 m3 (CGF)−1 with a mean and a median of 4.6 × 105 and 1.9 × 105 m3 (CGF)−1, respectively, during June–August 1993. The monthly rain volume per reported CG flash ranged from 6.3 × 104 to 2.1 × 105 m3 (CGF)−1 with an overall mean of 1.8 × 105 m3 (CGF)−1. Similar ratios were found for the Upper Mississippi River basin (UMRB) that is embedded within the GUMRB. For the entire summer season, there were about 6.5 × 1011 m3 of rainfall over the GUMRB and there were 3.6 × 106 CGF reported by the NLDN, which gives an overall seasonal mean of 1.8 × 105 m3 (CGF)−1. If the lightning counts are corrected for an imperfect NLDN detection efficiency, then it is estimated that there were actually about 5.4 × 106 CG flashes over the GUMRB, and therefore, the actual seasonal mean rain volume was about 1.3 × 105 m3 (CGF)−1. The above values are remarkably similar to the summer mean of 1.1 × 105 m3 (CGF)−1 obtained by Petersen and Rutledge over the midcontinental United States and are consistent with other studies on daily and storm scales. The above ratios are larger than, but still consistent with, an estimate of the excess stream volume per excess (reported) CG flash from the UMRB, 6.8 × 104 m3 (CGF)−1, based on streamflow measurements at Keokuk, Iowa.

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E. Philip Krider and R. Carl Noggle

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Broadband magnetic field antenna systems which can resolve submicrosecond structure in lightning waveforms are described. Correlated data on the magnetic and electric fields produced by distant lightning are presented and are shown to be, for the most part, identical in shape.

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Launa M. Maier, E. Philip Krider, and Michael W. Maier

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Data derived from a large network of electric field mills have been used to determine the average diurnal variation of lightning in a Florida seacoast environment. These data were obtained at the NASA Kennedy Space Center (KSC) and the Cape Canaveral Air Force Station (CCAFS) during the summers of 1976–78 and 1980 and they show a peak in lightning activity between the hours of 2000 and 2100 GMT or about 3 hours after local solar noon. When the statistics of lightning am compared with the statisfies or thunder on the same day, good agreement is round between the start times and the times of peak activity; however, the thunder stop times tend to Rag the lightning by 1 to 2 hours.

The average diurnal variation of cloud-to-ground lightning that was recorded by a network of magnetic diffusion-finders covering the entire South Florida region during the summer of 1978 is in good agreement with the results obtained at KSC and CCAFS and agrees with previous estimates of the time variations in rainfall and the rainfall rate over South Florida. The South Florida lightning data also show substantially less diurnal variation over the Atlantic Ocean and Gulf of Mexico than over the land. The implications of these results for the detection of lightning at local midnight dawn and dusk by a DMSP (Defense Meteorological Satellite Program) satellite are discussed.

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E. Philip Krider, R. Carl Noggle, and Martin A. Uman

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A magnetic direction finder has been developed which utilizes only the initial few microseconds of wide-band return stroke waveforms to provide accurate directions to the channel bases of lightning discharges to ground. Bearing errors are minimized because, near the ground, most channels tend to be straight and vertical with no large branches or horizontal sections. Tests on a number of lightning storms at distances of 10 to 100 km indicate the angular resolution is in the range from 1° to 2°, with little or no systematic dependence on azimuth or distance.

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Carlos Manuel Minjarez-Sosa, Christopher L. Castro, Kenneth L. Cummins, E. Philip Krider, and Julio Waissmann

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The relationship between convective precipitation and cloud-to-ground (CG) lightning is examined over a study area in southwest Arizona and northwest Mexico. Using seasonal-to-daily and hourly time resolution, the National Climatic Data Center (NCDC) stage IV precipitation product and the U.S. National Lightning Detection Network lightning data have been analyzed with the aim of developing an improved understanding of the relationship between these variables. A Gaussian method of spatially smoothing discrete lightning counts is used to estimate convective rainfall and improve the quality and spatial coverage of radar-derived precipitation in areas of complex terrain. For testing the dependence of the relationship between CG lightning and precipitation, a precipitation “sensor coverage” analysis has been performed. If locations that have poor sensor coverage are excluded, R 2 between lightning and precipitation improves by up to 15%. A complementary way to estimate convective precipitation is proposed based on 1-h lightning occurrence intervals, which is the maximum time resolution in this study. We find that ~67% of the seasonal 2005 precipitation over the analysis domain is associated with CG lightning. Daily precipitation estimates are improved by specifying a “diurnal day” based on the diurnal maxima and minima in precipitation and CG lightning within the domain. Our method for improving quantitative precipitation estimation (QPE) using lightning is able to track and estimate convective precipitation over regions that have poor sensor coverage, particularly in both air mass storms and large multicellular events, with R 2 up to 70%.

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Christina A. Stall, Kenneth L. Cummins, E. Philip Krider, and John A. Cramer

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Video recordings of cloud-to-ground (CG) lightning flashes have been analyzed in conjunction with correlated stroke reports from the U.S. National Lightning Detection Network (NLDN) to determine whether the NLDN is capable of identifying the different ground contacts in CG flashes. For 39 negative CG flashes that were recorded on video near Tucson, Arizona, the NLDN-based horizontal distances between the first stroke and the 62 subsequent strokes remaining in a preexisting channel had a mean and standard deviation of 0.9 ± 0.8 km and a median of 0.7 km. The horizontal distances between the first stroke and the 59 new ground contacts (NGCs) had a mean and standard deviation of 2.3 ± 1.7 km and a median of 2.1 km. These results are in good agreement with prior measurements of the random errors in NLDN positions in southern Arizona as well as video- and thunder-based measurements of the distances between all ground contacts in Florida. In cases where the distances between ground contacts are small and obscured by random errors in the NLDN locations, measurements of the stroke rise time, estimated peak current, and stroke order can be utilized to enhance the ability of the NLDN to identify strokes that produce new ground terminations.

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